If Nero refuses, do you really have any other choice? Can you afford for him to survive falling through another black hole? Kirk did what had to be done.
I can't stand the Academy portion of the film, personally.
I don't mind them firing afterward, it was more the way the offer was derided by the movie. As if capturing Nero and his crew was an inherently bad thing.
I was okay with the Academy stuff, personally, as I think it illustrated Kirk's Devil May Care attitude had some depth to it. He's not just a complete ass, he also has a "never say die" will that makes him a good captain.
Then again, I think Kirk 'cheating' was kind of ridiculous. It was really-really obvious he did.